MobileGrid: Capacity-aware Topology Control in Mobile Ad Hoc Networks

Transcription

1 MobleGrd: Capacty-aware Topology Control n Moble Ad Hoc Networks Jle Lu, Baochun L Department of Electrcal and Computer Engneerng Unversty of Toronto {jenne,bl}@eecg.toronto.edu Abstract Snce wreless moble ad hoc networks are arbtrarly and dynamcally deployed, the network performance may be affected by many unpredctable factors such as the total number of nodes, physcal area of deployment, and transmsson range on each node. Prevous research results only focus on maxmzng power effcency through dynamcally adjustng the transmsson range on each node. Va extensve performance evaluatons, we have observed that the network performance s lnked wth a sngle parameter, the network contenton ndex, whch each node may estmate n a fully dstrbuted fashon. Ths paper ntroduces the defnton of such a parameter, whch s derved from relevant parameters such as the number of nodes and the transmsson range on each node. Wth the presence of node moblty, we present a detaled study of the effects of contenton ndex on the network performance, wth respect to network capacty and power effcency. We have observed that the capacty s a concave functon of the contenton ndex. We further show that the mpact of node moblty s mnmal on the network performance when contenton ndex s hgh. Based on these mportant observatons, we present MobleGrd, a fully dstrbuted topology control algorthm that attempts to acheve the best possble network capacty, by mantanng optmal contenton ndex va dynamcally adjustng the transmsson range on each of the nodes n the network. I. INTRODUCTION In moble ad hoc networks, snce nodes are autonomc, t s practcally mpossble to predct the state of many mportant parameters wth tractable mathematcal models, ncludng () the total number of nodes; () the physcal area of deployment; and () the transmsson range on each node. However, such parameters dramatcally affect the network topology over tme, and consequently have a consderable mpact on the network performance, such as network capacty and power effcency. Maxmzng power effcency s prmarly acheved n prevous work by dynamcally adjustng the nodal transmsson range. They requre a statonary ad hoc network wthout node moblty, n order to use a tractable mathematcal model to derve the relatonshp between energy consumpton and nodal transmsson ranges. Such mathematcal models may be used to optmze the topology to conserve power. However, we argue that, the absolute value of transmsson range tself s not an ndependent drvng force that affects power effcency and network capacty. The fluctuatng number of nodes n the network and the physcal area of deployment also play a role. In order to dentfy one sngle parameter n controllng the network performance, we present a generc noton n ad hoc networks, the contenton ndex, whch represents the number of contendng nodes wthn the nterference range. In ths work, va extensve performance evaluatons, we contend that the contenton ndex, rather than the transmsson range on each node, s the prmary and ndependent drvng force that nfluences the network performance. Indeed, smulaton results show that network capacty s a concave functon of contenton ndex. As such, we argue that optmal values of contenton ndex do exst to acheve the best possble performance. Based on the above crtcal fndngs from performance evaluaton results, we propose MobleGrd, a dstrbuted topology control algorthm to ensure every node n a moble ad hoc network adjust the transmsson range to mantan an optmal contenton ndex whch may lead to a topology that yelds optmal performance n terms of network capacty. The most sgnfcant and novel contrbuton n ths paper that dstngushes t from prevous works s that, we perform onlne dynamc range adjustments not only for the purpose of conservng power, but also for the purpose of keepng other network Qualty of Servce (QoS) parameters checked, hopefully around ther optmal values achevable n the network. There exsts prevous work that consders throughput or delay when tunng transmsson ranges, but none of them has offered nsghts on the forward path of the closed loop,.e., how to adjust the ranges to acheve a better,orbest possble, throughput or delay. What we have contrbuted s the characterzaton of one of the nherent network propertes, the contenton ndex, that affects the network performance sngle-handedly, yet straghtforward to montor and estmate wth a fully dstrbuted algorthm. The remander of the paper s organzed as follows. After dscussng related work (Sec. II) and prelmnares (Sec. III), we dvde the paper nto two stages. In the frst stage (Sec. IV), we present extensve and convncng smulaton results to show the bond between the contenton ndex and network performance. In the second stage (Sec. V), we formally present MobleGrd, a smple, yet effectve, dstrbuted algorthm to control the topology n order to acheve better performance. Secton VII concludes the paper and ponts out possble future drectons. II. RELATED WORK Prevous studes on capacty of wreless networks have been reported n [], []. The network examned s statonary, wth unform node densty and fxed transmsson range. It has been shown that the per-node capacty may be estmated n the order of O(/ n), n beng the number of nodes n the network. However, the compensatng effects of local per-node transmsson range adjustments on the network performance (e.g. capacty) has yet to be studed. Elbatt et al. [] attempt to dynamcally reach a near-optmal operatng power level to maxmze the end-to-end throughput. By ncreasng a node s transmsson power untl the throughput starts decreasng, t works based on the assumpton that the

2 throughput s a concave functon of transmsson power. However, there s no theoretcal analyss or smulaton studes n [] to valdate ths assumpton. The nstantaneous throughput needs to be measured on an ongong bass usng an onlne algorthm, and the dynamc adjustments may be affected by shortterm throughput varatons. In comparson, we beleve that network capacty has an nherent bondng relatonshp wth the contenton ndex. Rather than adjustng the range to ncrease nstantaneous throughput, t may be more advantageous to fnd an optmal operatng pont that ncreases the capacty, even wth a network wthout much ongong packet transmssons present. Bansal et al. [4] shows that n a statonary ad hoc network, the overall power assumpton s a convex functon of the number of hops for end-to-end TCP sessons and n some cases, network capacty s a concave functon of transmsson range. Though the nsghts are nterestng, they are not used to drect the desgn of new protocols, leadng to a lack of the forward path to close the feedback loop. Towards ths end, we dentfy a parameter, the contenton ndex, that may be locally measured, rather than the node densty n the prevous work, whch may not be estmated locally. Further, rather than a statonary ad hoc network, we consder node moblty n all of our performance evaluatons. Grossglauser et al. [5] focus on a moble ad hoc network where the moblty pattern ensures that each node has the chance to eventually vst all other nodes n the network. As a result, at the expense of ncreased (possbly nfnte) end-to-end delay, node moblty may be used to acheve mult-user dversty, whch ncreases per-node throughput. In ths work, we do not study the ssue of delayed delveres,.e., ncreasng network capacty at the expense of end-to-end delay. The ssue of topology control has been extensvely addressed by prevous work. As one example, Wattenhofer et al. [6] have proposed a fully dstrbuted algorthm that only reles on drectonal nformaton between nodes to decde the mnmum transmsson power requred to ensure the connectvty of the network. However, the work does not consder other QoS parameters other than power effcency and basc network connectvty. All exstng work on topology control focus on power optmzaton n statonary wreless ad hoc networks, and do not consder the mpact on other performance parameters. In comparson, the emphass on optmal performance and consderaton of node moblty are the hghlghts of our work. III. THE CONTENTION INDEX In our performance evaluatons, we consder n moble nodes (equpped wth omn-drectonal antennas), each usng the transmsson range R, n a network deployed n an L by L square. We formally defne the contenton ndex as the number of nodes wthn the transmsson range (or the nterference range, f dfferent). Ths parameter s referred to as the contenton ndex snce t represents the potental congeston level n the local neghborhood. For the sake of smplcty and a functonal MAC protocol, we assume that the transmsson ranges on all nodes are dentcal. As such, the contenton ndex s related to three parameters n the smulaton setup: () the total number of nodes n; () the physcal area of deployment L ; and () the nodal transmsson range R. Naturally, the contenton n the network ncreases when there are more nodes n the network, or each node adopts a larger transmsson range, or the network area sze decreases. Wth the node densty D calculated as n/l, the contenton ndex, CI, s the product of node densty and area sze of local transmsson range: CI = DπR = nπr L () We vary the contenton ndex n the performance evaluatons as a prmary drvng force, n order to measure ts mpact on the performance of the network n terms of network capacty and power effcency. IV. PERFORMANCE EVALUATION We begn our studes by evaluatng the bondng relatonshps between varyng contenton ndces and QoS parameters n a moble ad hoc network. The ns.b8a network smulator s used to carry out the evaluatons. There are 6 nodes randomly deployed n an L by L area. The nodes move followng the random waypont moblty model supported by ns, where the nodes move at a bounded speed to a randomly selected destnaton wth a pause tme of seconds. The traffc load n such a network s set to be 6 ftp sessons on top of the TCP protocol such that node sends packets to node, node to node, and so on, tll node 5 to node. The power consumpton of the wreless nterface s set to be.95 W for recevng at all cases,.66 W for transmttng when the transmsson range s 5 meters, and vares lnearly wth the transmsson power. The contenton ndex CI vares wth ether one of the followng: () the area sze L whch s n the range of [, 658]m whle R = 5m; () the transmsson range R whch s n the range of [8, ]m whle L = 84m. The total number of nodes, n, s set as 6 for both scenaros. In all smulatons, we use IEEE 8. as the MAC protocol wth a channel capacty of Mb/s and Dynamc Source Routng as the routng algorthm. We smulate for 6 seconds. The network performance s evaluated by examnng two metrcs: () network capacty s defned as the total number of bytes of data successfully delvered to the destnatons per tme unt n the entre network; () power effcency s measured by the energy (n Joules) consumed for each successfully delvered packet. We present the results of performance evaluaton wth respect to the the effects of contenton ndex and node moblty speed on network performance. A. Network Capacty The bondng relatonshps between the contenton ndex and the network capacty s presented n Fg. and Fg.. Both dagrams use natural logarthmc scale to show the axs of contenton ndex. As llustrated n the fgures, we observe that the network capacty s a concave functon of the contenton ndex at a certan bounded speed. It s observed that when contenton ndex CI vares wth L or R, the network capacty s maxmzed when CI s between and 9. When CI s less than, the network s sparse such that many transmtted packets are dropped at the network layer due to non-exstence of routes. Typcally, when CI =, among the

3 .5 Speed= m/s Speed= m/s.6.5 Speed= m/s Speed= m/s Network Capacty (Mb/s).5 Power Effcency (Joules/pkt) Fg.. Network Capacty vs. Contenton Index (L vares) Fg.. Power Effcency vs. Contenton Index (R vares).8.6 Speed= m/s Speed= m/s Speed= m/s Speed= m/s Network Capacty (Mb/s) Average Path Length (Hops/pkt) Fg.. Network Capacty vs. Contenton Index (R vares) Fg. 4. Average Path Lengths vs. Contenton Index (R Vares) dropped packets, 9% occurs durng routng and only % happens at the lnk layer. In comparson, when CI =5,.5% of dropped packets are at the network layer and 87.5% occurs at lnk layer. Ths llustrates the trade-off between havng weak connecton at low CI and hgh contenton n the shared channel at hgh CI. The optmzaton s acheved when CI s n [, 9] such that the network capacty s maxmzed. The above observaton holds when CI s vared wth ether L or R, whch leads to the concluson that contenton ndex s the prmary drvng force to affect network capacty rather than transmsson range R tself. Addtonal smulaton results have shown that, despte that fact that network capacty decreases wth the hgher moblty speed when CI s low, the moblty speed tends to have mnmal mpact on network capacty when CI s hgher than. No matter what the speed s, the network capacty s maxmzed when CI s n [, 9]. B. Power Effcency Fg. depcts the relatonshp between contenton ndex (n ln CI) and power effcency. It s perceved that when CI s n [, 9] such that network capacty s maxmzed, the power effcency s close to optmal. In addton, when CI s lower than, the power consumpton s the lowest at the cost of a low network capacty. Ths s because when CI <, the average hops of packet traverse s n [,.] as n Fg. 4, whch means t s m- possble to establsh a mult-hop path between source and destnaton n such a sparse network wth the presence of node moblty. Successful packet transmsson may only occur between two nearby nodes. Moreover, the transmsson range at ths state s short. As a result, the power effcency s pretty hgh. On the other hand, when CI > 9, the average path length of successfully transmtted packet s also n the range [,.] as n Fg. 4. However, ths mnmal length s acheved by havng nodes employ a large transmsson power whch also cause collsons at the network lnk layer and subsequently more re-transmssons. As a result, power effcency s low. From the above results, we can conclude wth the followng observatons. Frst, the network capacty s a concave functon of the contenton ndex and s maxmzed when contenton ndex s n [, 9]. Second, the power effcency s a half convex functon of contenton ndex, and s close to optmal when the contenton ndex s the same range [, 9]. Thrd, the range of optmal contenton ndces does not change wth moblty speed. Fnally, the moblty speed of nodes do have mnor mpact on network performance wth respect to network capacty and power effcency when CI. We conclude wth the statement that, t s the contenton ndex, rather than the transmsson range on each node, that s the prmary and ndependent drvng force that nfluences the network performance. Ths result holds for QoS parameters such as the network capacty and power effcency. We note that, n

4 4 real-world ad hoc networks, due to the dversty of the physcal, MAC and routng layer protocols and parameters, the actual optmal contenton ndex may not be dentcal as was observed n ths secton. However, our concluson stll holds n that: () there exst an optmal value of contenton ndex correspondng to a specfc QoS parameter; and () such optmal value may be measured usng off-lne experments, and s an nherent property that wll not change over the lfespan of the network. Such nsghts promote our work to desgn a fully dstrbuted topology control algorthm to acheve the best possble network performance, wth respect to at least one of the network parameters. By tunng the transmsson ranges on each of the nodes, we have effectvely adjusted and mantaned the contenton ndex around ts optmal values. Wth ths dea, we next present the Moble- Grd algorthm. V. MOBILEGRID ALGORITHM We now propose a smple, yet effectve, dstrbuted topology control algorthm, MobleGrd, for nodes n moble ad hoc networks to make fully localzed decsons on the optmal transmsson range to mantan an optmal contenton ndex, so that the network capacty s optmzed. It s hard for a node to compute the network contenton ndex usng Eq. () accurately, due to the lack of global knowledge on ether the number of nodes or the physcal area of deployment. Even f t manages to obtan such knowledge, the communcaton and computaton cost of dynamcally updatng the knowledge s overwhelmng, whch the nodes can ll afford. That sad, snce n/l s the number of nodes per unt area and πr s the rado coverage area of a node, we know that the average number of nodes n a node s transmsson range, N, s gven by N = n/l πr =CI. Thus, by knowng how many neghbors a node has, the node can estmate the contenton ndex. Based on ths observaton, our dstrbuted topology control algorthm, MobleGrd, s mplemented as a three-phase protocol, executed at each node perodcally (by the end of each tme wndow) to accommodate node moblty. Phase. Estmatng Contenton Index A node starts to dscover ts neghbors at the MAC layer wth ts current transmsson power (or maxmum power at th tme wndow) by overhearng both control (e.g. RTS/CTS/ACK) and data messages. Snce the header of each message contans the source node ID, the node may compute the number of unque node IDs that t may overhear over the tme wndow. Such a set of unque node dentfers forms the set of neghbors that the node may fnd. Such a passve approach does not ntroduce addtonal overhead to the exstng network traffc. Obvously the node may not be able to detect slent nodes n the neghborhood that dd not transmt any control or data messages. We argue that, snce such slent nodes dd not nject network traffc n the current tme wndow, the possblty that they start to transmt n the next tme wndow s low. In ths case, the calculaton of contenton ndex may safely gnore such nodes. As dscussed earler, f the dscovered number of neghborng nodes s N, the estmated contenton ndex CI s N +. Phase. Lookng up Optmal Values of the Contenton Index =max =ms t t t Fg. 5. Tme Sequence at Node Each node looks up n a partcular optmzaton table to determne f t s operatng around an optmal value of contenton ndex. The table stores the optmal values of contenton ndex to maxmze the network capacty, whch we may obtan from off-lne experments usng dentcal physcal, MAC and routng layer characterstcs and parameters. Snce the optmal contenton ndex s an nherent property that does not vary much when changng node moblty, we may safely assume that such an optmzaton table may not need to be updated frequently. Wth respect to an nterested QoS parameter such as network capacty, f the contenton ndex t has estmated from the frst phase does not fall nto the specfc optmal range n the table, the node proceeds to the next phase to adjust ts transmsson range. Otherwse, the current transmsson range s adopted for the next tme wndow. Phase. Transmsson Range Adjustments If, n the second phase, a node decdes that ts current transmsson range s not optmal by a table look-up, t uses the followng scheme to eventually keep t checked wthn the range of optmal contenton ndex values. If the contenton ndex CI calculated n the frst phase s out of the optmal range n the optmzaton table (ether smaller than the lower bound or hgher than the upper bound), the node tunes the transmsson power R as llustrated n Eq. (): CIoptmal Rnew = mn( R current,r max ) () CI current where Rmax s the maxmum transmsson range decded by the physcal layer and rado characterstcs, and CI optmal s chosen as the medan pont of the optmal range n the table. Ths scheme guarantees convergence towards ether the maxmum range Rmax, or the optmal range of contenton ndces, whchever appears earler. Fg. 5 llustrates the tme sequence at node. The notaton k represents the transmsson power of node at kth tme wndow; k stands for the length of tme wndow at node at the kth tme wndow; t k s the executon tme of Phase and Phase MobleGrd algorthm at node by the end of kth tme wndow. Intally, at tme, node uses the maxmum transmsson power R max to buld ts neghbors lst over the ntal tme wndow whch s a random number between ms and ms (or other representatve values). Upon the expry of, node spends t tme on the table look-up and adjustng the transmsson power accordng to the MobleGrd algorthm. Meanwhle, t calculates the duraton of the next tme wndow. Sequentally, node uses the resulted as transmsson range, and T w as tme wndow for next teraton. The calculaton of tme wndow Tw k+ by the end of kth t

5 5 5 Central Soluton MobleGrd Algorthm 4 Central Soluton MobleGrd Algorthm 5 Average Transmsson Range 5 Standard Devaton of Transmsson Range Number of Nodes ( n ) Number of Nodes ( n ) Fg. 6. Centralzed Soluton vs. MobleGrd (Average Transmsson Range) tme wndow s to mnmze the probablty of occurrences of the race condton between tself and neghborng nodes, denoted as P conf. Gven that node has N neghborng nodes, P conf = N j= ( t k+ j T k+ wj +tk+ j t k+ T k+ w +t k+ ). To smplfy the problem and reduce overhead, node assumes t requres the same t durng dfferent teratons and surroundng nodes employ smlar T w and t as tself. It may be derved that N w ( )t k Pconf T k+ To conclude, regardng the transmsson range adopted by node n varous teratons runnng the MobleGrd algorthm, we have: { max k =; R k = mn( CIoptmal CI k R k,r max ) k. VI. EXPERIMENTS ON THE MOBILEGRID ALGORITHM In order to evaluate f MobleGrd works as effectve as the centralzed soluton n prevous performance evaluatons (Sec. IV), we use a snapshot of a wreless ad hoc network n an area of 5 meters by 5 meters where each node s maxmum transmsson range s meters. The number of nodes n such a network vares from to. Network capacty s chosen to be optmzed and the optmal contenton ndex CI s set to be 6. Both the average transmsson power and standard devaton of transmsson powers are measured n the experments, where average transmsson power s calculated as the sum of transmsson powers at each node dvded by number of nodes n the network, the standard devaton of transmsson powers s calculated to demonstrate how dverse are the transmsson ranges among all network nodes. Fg. 6 demonstrates the respectve average transmsson range n the resulted topology based on the centralzed soluton and MobleGrd algorthm, respectvely. We observe that the two curves are very close to each other, whch means that MobleGrd performs nearly as well as the centralzed soluton. Furthermore, ths observaton does not change wth the total number of nodes. In the centralzed soluton, all nodes are supposed to adopt a unform transmsson range. Hence, n Fg. 7, the curve for the Fg. 7. Centralzed Soluton vs. MobleGrd (Standard Devaton of Transmsson Ranges) centralzed soluton s flat wth values of. However, n MobleGrd, the standard devaton of transmsson powers s always postve snce the network s not evenly dstrbuted, dfferent nodes adopts dfferent powers to cover the same number of neghborng nodes. As we may observe, the standard devaton of transmsson powers tends to declne wth the denser nodes n the network. VII. CONCLUSIONS In ths paper, we ntroduce an nterestng decsve parameter, contenton ndex, wthn the scope of moble ad hoc networks. Va extensve performance evaluatons, t s found that the contenton ndex s the prmary drvng force that nfluences the network performance wth respect to network capacty and power effcency. Furthermore, optmal values of the contenton ndex does exst to optmze the network performance. MobleGrd, a dstrbuted topology control algorthm, s proposed to ensure optmalty regardng the contenton ndex. It s proved to be effectve by our smulaton results. REFERENCES [] P. Gupta and P. R. Kumar, The Capacty of Wreless Networks, vol. 46, no., pp , March. [] J. L, C. Blake, D. S. J. De Couto, H.I.Lee, and R. Morrs, Capacty of Ad Hoc Wreless Networks, n Proceedngs of the 7th ACM Internatonal Conference on Moble Computng and Networkng, Rome, Italy, July, pp [] T. A. ElBatt, S. V. Krshnamurthy, D. P. Connors, and S. Dao, Power Management for Throughput Enhancement n Wreless Ad-Hoc Networks, n Proceedngs of IEEE ICC, New Orleans,, pp [4] S. Bansal, R. Gupa, R. Shorey, I. Al, A. Razdan, and A. Msra, Energy Effcency and Throughput for TCP Traffc n Mult-Hop Wreless Networks, n INFOCOM,. [5] M. Grossglauser and D. Tse, Moblty Increases the Capacty of Ad-Hoc Wreless Networks, n Proceedngs of INFOCOM,. [6] R. Wattenhofer, P. Bahl L. L, and Y. M. Wang, Dstrbuted Topology Control for Power Effcent Operaton n Multhop Wreless Ad Hoc Networks, n Proceedngs of INFOCOM, Aprl.